Minimum Average Distance Triangulations

Some of the following problems look similar to the MAD Triangulation problem, but we have not found any deep connections: •Minimum Average Distance Spanning Subgraph in a budgeted version [2] was studied in the context of network design (minimizing average routing time). The problem is NP-complete even with unit weights. •Minimum Average Distance Spanning Tree [1]. NP-completeness is implied by the previous result. • In chemistry W(T ) is known as Wiener-index [3] and if it is computed for molecular structures, it correlates with chemical properties of materials [4]. There has been significant research on efficiently computing W(T ) for special graphs [5,6] and on combinatorial properties of W(T ) [7] when edges have unit weight. •Minimum Weight Triangulation known to be NP-hard [8]. •Minimum Dilation Triangulation known to be NP-hard [9].